This preview shows pages 1–13. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Optical Resonator Modes ECE 455 Optical Electronics Tom Galvin Gary Eden ECE Illinois ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Introduction In this section, we will learn how to do the following things: ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B ABCD Matrix I The ABCD matrix is a ray optics formalism relates the distance r from the optical axis and its slope r of a ray as is propogates through optical elements. Assumptions ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B ABCD Matrix II Position above optic axis and slope are represented by a vector r r (1) Cummulative effect of optical elements are matrices A B C D (2) To find the position and slope of a ray after propogating through an optical system use r 2 r 2 = A B C D r 1 r 1 (3) ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B ABCD Matrix III Beware! Different books (notably Hecht and Siegman) use different conventions for ABCD matrices than defined in the previous page. Some switch the position of r and r . Another possible convention is to multiply the slope by the refractive index. ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Uniform Dielectric distance d Diagram d Axis ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Uniform Dielectric distance d It should should be clearly obvious that ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Thin Lens Diagram Axis ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Thin Lens The ABCD matrix of the thin lens can be derived as follows: ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Spherical Mirror Diagram r R = 2f f 1 2 ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Spherical Mirror The spherical mirror is identical to the case of a thin lens. Recall that the focus of a spherical mirror with radius R is f = R 2 (10) The result of the thin lens can then be used with the appropriate value substituted in place of f A B C D = 1 2 R 1 (11) ECE 455 Lecture 2 ABCD Matrix Cavity Stability Gaussian Beams Q, F and Photon Lifetime Summary Appendix A Appendix B Flat Mirror Consider the ABCD matrix of a spherical mirror....
View Full
Document
 Fall '08
 Eden,J

Click to edit the document details